Flaws in robust optimistic mix-nets and stronger security notions

Contribution of this paper is twofold: First we introduce weaknesses of two Mix-nets claimed to be robust in the literature. Since such flaws are due to their weak security definitions, we then present a stronger security definition by regarding a Mix-net as a batch decryption algorithm of a CCA secure public-key encryption scheme. We show two concrete attacks on the schemes proposed in [1] and [2]. The scheme in [1] loses anonymity in the presence of a malicious user even though all servers are honest. The scheme in [2] also loses anonymity through the collaboration of a malicious user and the first server. In the later case the user can identify the plaintext sent from the targeted user by invoking two mix sessions at the risk of the colluding server receiving an accusation. We also point out that in a certain case, anonymity is violated solely by the user without colluding to any server. Heuristic repairs are provided for both schemes.